Optimal. Leaf size=21 \[ \log \left (\left (-1+3 x+256 x^2\right ) \left (-x^2+\log (\log (x))\right )\right ) \]
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Rubi [A]
time = 0.92, antiderivative size = 22, normalized size of antiderivative = 1.05, number of steps
used = 5, number of rules used = 4, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.047, Rules used = {6873, 6860,
642, 6816} \begin {gather*} \log \left (-256 x^2-3 x+1\right )+\log \left (x^2-\log (\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rule 6816
Rule 6860
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+3 x+256 x^2+\left (2 x^2-9 x^3-1024 x^4\right ) \log (x)+\left (3 x+512 x^2\right ) \log (x) \log (\log (x))}{x \left (1-3 x-256 x^2\right ) \log (x) \left (x^2-\log (\log (x))\right )} \, dx\\ &=\int \left (\frac {3+512 x}{-1+3 x+256 x^2}+\frac {-1+2 x^2 \log (x)}{x \log (x) \left (x^2-\log (\log (x))\right )}\right ) \, dx\\ &=\int \frac {3+512 x}{-1+3 x+256 x^2} \, dx+\int \frac {-1+2 x^2 \log (x)}{x \log (x) \left (x^2-\log (\log (x))\right )} \, dx\\ &=\log \left (1-3 x-256 x^2\right )+\log \left (x^2-\log (\log (x))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.30, size = 22, normalized size = 1.05 \begin {gather*} \log \left (1-3 x-256 x^2\right )+\log \left (x^2-\log (\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.24, size = 23, normalized size = 1.10
method | result | size |
risch | \(\ln \left (256 x^{2}+3 x -1\right )+\ln \left (\ln \left (\ln \left (x \right )\right )-x^{2}\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 22, normalized size = 1.05 \begin {gather*} \log \left (256 \, x^{2} + 3 \, x - 1\right ) + \log \left (-x^{2} + \log \left (\log \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 22, normalized size = 1.05 \begin {gather*} \log \left (256 \, x^{2} + 3 \, x - 1\right ) + \log \left (-x^{2} + \log \left (\log \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 20, normalized size = 0.95 \begin {gather*} \log {\left (- x^{2} + \log {\left (\log {\left (x \right )} \right )} \right )} + \log {\left (256 x^{2} + 3 x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 22, normalized size = 1.05 \begin {gather*} \log \left (256 \, x^{2} + 3 \, x - 1\right ) + \log \left (-x^{2} + \log \left (\log \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.34, size = 22, normalized size = 1.05 \begin {gather*} \ln \left (\ln \left (\ln \left (x\right )\right )-x^2\right )+\ln \left (256\,x^2+3\,x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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